{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YB7NXJWNWFNGY6TCWIGU4J5JLG","short_pith_number":"pith:YB7NXJWN","canonical_record":{"source":{"id":"1104.3900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-19T23:19:15Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"509796f04effcdd832003e06c59909e7710afe5452d4a278d7d5134c006b5d7f","abstract_canon_sha256":"00d228f4df9eab5f67f6549c80bff76020121321ec687521b5322fb8b83b0954"},"schema_version":"1.0"},"canonical_sha256":"c07edba6cdb15a6c7a62b20d4e27a959a140d5147e35bf146fc487679ce067fd","source":{"kind":"arxiv","id":"1104.3900","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3900","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3900v1","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3900","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"YB7NXJWNWFNG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YB7NXJWNWFNGY6TC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YB7NXJWN","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YB7NXJWNWFNGY6TCWIGU4J5JLG","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-19T23:19:15Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"509796f04effcdd832003e06c59909e7710afe5452d4a278d7d5134c006b5d7f","abstract_canon_sha256":"00d228f4df9eab5f67f6549c80bff76020121321ec687521b5322fb8b83b0954"},"schema_version":"1.0"},"canonical_sha256":"c07edba6cdb15a6c7a62b20d4e27a959a140d5147e35bf146fc487679ce067fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:47.495562Z","signature_b64":"Cno4TE70Urm6mxBysboZTHwHK6ll+11uaXDKVLxTmuZjz1BCeNr2L7zLrD4+Ktb5mW8WT4S3VoFhONAtJDFCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c07edba6cdb15a6c7a62b20d4e27a959a140d5147e35bf146fc487679ce067fd","last_reissued_at":"2026-05-18T04:23:47.495024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:47.495024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3900","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGEbpznzZidq5o474dI4k5Z6hVNE7D+IimhcHFWZdoYf0MyAIPPDIhZYtmDcyk8kr4ZDjC7+jhJYdA6wImQJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:35:07.469680Z"},"content_sha256":"516b3a17eb64d40c52df036f4d1ae3107f293f83d19f4454e5071ee9f4721fe3","schema_version":"1.0","event_id":"sha256:516b3a17eb64d40c52df036f4d1ae3107f293f83d19f4454e5071ee9f4721fe3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YB7NXJWNWFNGY6TCWIGU4J5JLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diophantine Equations of Matching Games I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Chun Yin Hui, Wai Yan Pong","submitted_at":"2011-04-19T23:19:15Z","abstract_excerpt":"We solve a family of quadratic Diophantine equations associated to a simple kind of games. We show that the ternary case, in many ways, is the most interesting and the least arbitrary member of the family."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3900","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xNG1L7fphKGDHaOl50wWf3r/pGopK3xp7wWtZsE8o1E+HDPvVM41v1ZJJfXiYszY41Tr+jQKM+SD82KCXWIeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:35:07.470428Z"},"content_sha256":"27420d6184584f41fadd4a9d5f0dae25e47d0e724dcf439bf3025431349b167b","schema_version":"1.0","event_id":"sha256:27420d6184584f41fadd4a9d5f0dae25e47d0e724dcf439bf3025431349b167b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/bundle.json","state_url":"https://pith.science/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T19:35:07Z","links":{"resolver":"https://pith.science/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG","bundle":"https://pith.science/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/bundle.json","state":"https://pith.science/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YB7NXJWNWFNGY6TCWIGU4J5JLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YB7NXJWNWFNGY6TCWIGU4J5JLG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00d228f4df9eab5f67f6549c80bff76020121321ec687521b5322fb8b83b0954","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-19T23:19:15Z","title_canon_sha256":"509796f04effcdd832003e06c59909e7710afe5452d4a278d7d5134c006b5d7f"},"schema_version":"1.0","source":{"id":"1104.3900","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3900","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3900v1","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3900","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"YB7NXJWNWFNG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YB7NXJWNWFNGY6TC","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YB7NXJWN","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:27420d6184584f41fadd4a9d5f0dae25e47d0e724dcf439bf3025431349b167b","target":"graph","created_at":"2026-05-18T04:23:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We solve a family of quadratic Diophantine equations associated to a simple kind of games. We show that the ternary case, in many ways, is the most interesting and the least arbitrary member of the family.","authors_text":"Chun Yin Hui, Wai Yan Pong","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-19T23:19:15Z","title":"Diophantine Equations of Matching Games I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3900","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:516b3a17eb64d40c52df036f4d1ae3107f293f83d19f4454e5071ee9f4721fe3","target":"record","created_at":"2026-05-18T04:23:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00d228f4df9eab5f67f6549c80bff76020121321ec687521b5322fb8b83b0954","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-19T23:19:15Z","title_canon_sha256":"509796f04effcdd832003e06c59909e7710afe5452d4a278d7d5134c006b5d7f"},"schema_version":"1.0","source":{"id":"1104.3900","kind":"arxiv","version":1}},"canonical_sha256":"c07edba6cdb15a6c7a62b20d4e27a959a140d5147e35bf146fc487679ce067fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c07edba6cdb15a6c7a62b20d4e27a959a140d5147e35bf146fc487679ce067fd","first_computed_at":"2026-05-18T04:23:47.495024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:47.495024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cno4TE70Urm6mxBysboZTHwHK6ll+11uaXDKVLxTmuZjz1BCeNr2L7zLrD4+Ktb5mW8WT4S3VoFhONAtJDFCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:47.495562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3900","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:516b3a17eb64d40c52df036f4d1ae3107f293f83d19f4454e5071ee9f4721fe3","sha256:27420d6184584f41fadd4a9d5f0dae25e47d0e724dcf439bf3025431349b167b"],"state_sha256":"5920ae7c56f4e45964309f04525ac07846e7e2de6d7ae26b23d77ed59f8a01b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXdmLyMXZEmCTtHgoLQtdaCE3M58/AV+26cKTE72JjibLMIlo8hezP0fGsliLvzpfVi7mKtZ+WU9KrTzR+KOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:35:07.474137Z","bundle_sha256":"b0cd79bb528f9ca15f3e0fb287536fdfdd8056f2dd5145f36d7a193a4b7be0f1"}}